How to Report and Interpret Statistical Results
Choosing the right statistical test is only half the work — the results still have to be reported clearly and interpreted honestly once the analysis is done. Many results chapters and manuscripts run into trouble not because the analysis itself was wrong, but because the write-up buries the finding in raw software output, leaves out an effect size, or blurs the line between reporting what was found and interpreting what it means. This guide covers the standard conventions for reporting statistical results and organizing them so a reader can follow what you found and why it matters.
Report each result in a consistent format: what you tested, the test statistic, degrees of freedom, the exact p-value, and an effect size — organized by research question or hypothesis, not by which test happens to have been run. Keep interpretation out of the results section itself: state what you found there, and save what it means for the discussion. Report effect sizes and non-significant results alongside significant ones, and use the exact p-value (for example, p = .032) rather than only p < .05, switching to p < .001 only when your software rounds the value to .000.
Reporting Results vs. Interpreting Them
A results section and a discussion section do different jobs, and mixing them up is one of the most common structural mistakes in a results chapter or manuscript. The results section states what was found — the test used, the statistic, and whether it was significant — without explaining why it happened or what it means for the field. That explanation, along with limitations and broader implications, belongs in the discussion. Keeping the two separate makes it easier for a reader to check your findings against your claims about them.
The Standard Elements of a Reported Result
Most reporting conventions (APA style is the most widely used, though journals and disciplines vary in specifics) ask for the same core elements every time a test is reported: the symbol for the statistic (italicized, such as t, F, or r), the degrees of freedom in parentheses, the statistic's value to two decimal places, the exact p-value to three decimal places, and an effect size. Leaving any of these out — reporting only 'significant at p < .05' with no statistic or effect size — is one of the most common gaps reviewers and committees flag.
Reporting Descriptive Statistics First
Before any inferential test result, a results section typically reports descriptive statistics for the sample and key variables: sample size, means and standard deviations for continuous variables, or frequencies and percentages for categorical ones. These numbers give a reader the context needed to judge an inferential result — a statistically significant difference between two means is read very differently depending on how large or variable those means actually were.
Reporting t-Tests and ANOVA
A t-test is typically reported as t(degrees of freedom) = value, p = value, alongside the means and standard deviations being compared and an effect size such as Cohen's d. An ANOVA result adds an F-statistic with two degrees-of-freedom values, F(df between, df within) = value, p = value, plus an effect size such as eta-squared (η²). When an ANOVA is significant, it's followed by post-hoc test results identifying which specific groups differ, since the omnibus F-test alone only shows that some difference exists somewhere among the groups.
Reporting Correlation and Regression
A correlation is usually reported as r(degrees of freedom) = value, p = value, with the sign and size of r indicating direction and strength of the association. Regression results typically report each predictor's coefficient (B or β), its significance test, and the model's overall fit (R² or adjusted R²), which indicates how much variance in the outcome the predictors jointly account for. A common mistake is reporting a strong correlation as if it demonstrated causation, which correlation alone cannot establish.
Reporting Chi-Square and Non-Parametric Tests
A chi-square test of independence is typically reported as χ²(degrees of freedom, N = sample size) = value, p = value, with an effect size such as Cramér's V for larger tables. Non-parametric alternatives — Mann-Whitney U, Wilcoxon signed-rank, or Kruskal-Wallis — follow the same underlying logic (statistic, relevant sample-size information, p-value, effect size) even though the specific symbols and degrees-of-freedom conventions differ from their parametric counterparts.
Why Effect Sizes Aren't Optional
A p-value only indicates whether an effect is unlikely to be due to chance — it says nothing about how large or practically meaningful that effect is, especially in a large sample where even a trivial difference can reach statistical significance. An effect size (Cohen's d, eta-squared, r, or R², depending on the test) reports the actual magnitude of the effect, which is why most current reporting standards treat it as a required part of the result, not an optional extra.
Exact p-Values vs. Threshold Reporting
Current reporting conventions generally call for the exact p-value to three decimal places (for example, p = .032) rather than only stating that a result cleared a threshold like p < .05, since the exact value gives a reader more information. The one common exception is when statistical software rounds a very small p-value to .000, in which case it's reported as p < .001 rather than the technically impossible p = .000. Leading zeros are also dropped in APA-style reporting: p = .032, not p = 0.032.
Organizing Results by Research Question, Not by Test
A results section reads more clearly when it's organized around the research questions or hypotheses in the order they were introduced earlier in the document, rather than grouped by which statistical test happened to be used for each one. For each question, the typical pattern is: briefly restate what was tested, confirm any relevant assumption checks were met, report the test result in full, and note in one plain-language sentence what the number shows — without yet interpreting its broader meaning.
Using Tables and Figures Instead of Restating Every Number
Once several variables or multiple tests are involved, a table summarizing means, standard deviations, and test statistics is usually easier to follow than the same numbers repeated in full sentences throughout the text. The surrounding prose should highlight the pattern the table or figure shows rather than restating every value it already contains — a reader should be able to find the specific number in the table while reading the text's summary of what it means at a glance.
Common Mistakes When Reporting Statistical Results
The most frequent problems are: reporting only whether a result was significant without the statistic, degrees of freedom, or exact p-value; omitting effect sizes entirely; silently dropping non-significant results instead of reporting them alongside significant ones; interpreting or discussing a finding's implications inside the results section instead of saving that for the discussion; and pasting raw statistical-software output directly into a document instead of translating it into the standard reporting format.
When to Get Support Interpreting and Writing Up Your Results
Getting a second, statistically literate read on a results section — checking that every test is reported in the standard format, that effect sizes and non-significant findings weren't dropped, and that interpretation hasn't crept into a section meant to just report facts — is a common point to bring in outside support, particularly close to a submission or defense deadline when it's easy to miss these details in your own draft.
Frequently asked questions
Yes — current reporting conventions treat effect size as a required part of the result, not optional. A p-value shows whether an effect is unlikely to be due to chance, but the effect size shows how large or meaningful it actually is.
Report the exact p-value to three decimal places (p = .032) rather than only a threshold. The one exception is when your software rounds a very small value to .000, in which case p < .001 is the standard way to report it.
The results section reports what was found — the statistic, whether it was significant, and the effect size — without explaining why. Interpreting what a finding means, its limitations, and its broader implications belongs in the discussion.
Yes — reporting only significant findings and omitting non-significant ones is a form of selective reporting. A complete results section reports every planned analysis, significant or not.
Yes — explaining results in plain language alongside the raw output, and helping you report them in the standard format for your results chapter or manuscript, is part of our statistical and data analysis support.
References
- University of Washington Psychology Writing Center — Reporting Results of Common Statistical Tests in APA Format
A reference guide to the standard APA format for reporting t-tests, ANOVA, correlation, regression, and chi-square results.
- Hanover College — Writing a Results and Discussion
A university guide to structuring a results section and distinguishing it from the discussion that follows.
- Statoria — How to Write the Statistics Results Section of Your Thesis
A walkthrough of organizing and writing a thesis statistics results section by research question.
- Statoria — APA Statistics Reporting: Templates for Common Tests
Reporting-format templates for common statistical tests in APA style.